Techniques used to prove concentration of a measure include martingale methods, exchangeable pairs (e.g., see [1]}) and functional inequalities (transportation-entropy, logarithmic Sobolev/hypercontractivity and Poincare) [2]}. However, exploring measure concentration for dependent random variables as in Markov chains on unbounded spaces limits the application of martingale methods and exchangeable pairs. RL and system identification community, pretty much exclusively, have used independent block technique [3]}, [4]} that seems to work when observables are bounded. SLDS fall into the category of Markov chains admitting a Lyapunov function with geometric drift condition. Following [5]}, by using martingale and independent block techniques, authors in [6]} were able to bound the mean-squared error between the empirical average and the expected reward (unbounded) from stationary distribution of SLDS; however, the employed probabilistic methods are tedious, opaque and lead to weak results.
